# Properties

 Label 171462.n Number of curves 6 Conductor 171462 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("171462.n1")

sage: E.isogeny_class()

## Elliptic curves in class 171462.n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
171462.n1 171462i6 [1, 1, 1, -46637699, -122609077153] [2] 8519680
171462.n2 171462i4 [1, 1, 1, -2914889, -1916632429] [2, 2] 4259840
171462.n3 171462i5 [1, 1, 1, -2763599, -2124262825] [2] 8519680
171462.n4 171462i2 [1, 1, 1, -191669, -26717749] [2, 2] 2129920
171462.n5 171462i1 [1, 1, 1, -57189, 4858155] [2] 1064960 $$\Gamma_0(N)$$-optimal
171462.n6 171462i3 [1, 1, 1, 379871, -154971325] [2] 4259840

## Rank

sage: E.rank()

The elliptic curves in class 171462.n have rank $$0$$.

## Modular form 171462.2.a.n

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} + q^{4} - 2q^{5} - q^{6} + q^{8} + q^{9} - 2q^{10} + 4q^{11} - q^{12} + 2q^{13} + 2q^{15} + q^{16} - q^{17} + q^{18} - 4q^{19} + O(q^{20})$$

## Isogeny matrix

sage: E.isogeny_class().matrix()

The $$i,j$$ entry is the smallest degree of a cyclic isogeny between the $$i$$-th and $$j$$-th curve in the isogeny class, in the LMFDB numbering.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels.